Yes, they are correct.
No, you cannot get a corrected W-2 since they actually withheld and made ALL of the payments to NJ and nothing to PA.
So you will need to file a NJ return and allocate your income based on the time you lived in NJ and file the PA return and allocate your income based on the time you lived in PA. You will end up having to pay PA since they did not withhold for PA. But you will get a refund of NJ.
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